P. M. Rakotomamonjy

activity

20182022

collaborators

4 papers

math.CO2022

Combinatorial of restricted permutations according to the number of crossings

Paul Mazoto Rakotomamonjy

In this thesis, we introduced and carried out a combinatorial study of permutations that avoid one or two patterns of length 3 according to the statistic number of crossings. For t…

math.CO2019

Crossings over permutations avoiding some pairs of patterns of length three

Paul M. Rakotomamonjy, Sandrataniaina R. Andriantsoa, Arthur Randrianarivony

In this paper, we compute the distributions of the statistic number of crossings over permutations avoiding one of the pairs ${321, 231}$ , ${123, 132}$ and ${123, 213}$ . The obt…

math.CO2019

New combinatorial interpretations of the binomial coefficients

Paul M. Rakotomamonjy, Sandrataniaina R. Andriantsoa

Using generating functions and some trivial bijections, we show in this paper that the binomial coefficients count the set of (123,132) and (123,213)-avoiding permutations accordin…

math.CO2018

Restricted permutations refined by number of crossings and nestings

Paul M. Rakotomamonjy

Let $s t = {s t_{1}, \dots, s t_{k}}$ be a set of $k$ statistics on permutations with $k \geq 1$ . We say that two given subset of permutations $T$ and $T^{'}$ are $s t$ -Wilf-equivalent if the j…